Related papers: Improved lower and upper bounds on the tile comple…
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity measure for primal--dual metrics at pairs of primal and dual…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Active particles locally transduce energy into motion, leading to unusual and emergent behaviors. However, current synthetic particles lack sensing and adaptation mechanisms. Here, we demonstrate a novel regulation pathway, through the…
In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can…
We give a deterministic nearly-linear time algorithm for approximating any point inside a convex polytope with a sparse convex combination of the polytope's vertices. Our result provides a constructive proof for the Approximate…
We study the recently-introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for $d = 1$, or a directed surface…
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain…
We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of…
This study presents a comprehensive investigation into the exceptional superconducting attributes of titanium nitride (TiN) achieved through plasma-enhanced atomic layer deposition (PEALD) on both planar and intricate three-dimensional (3D)…
Given a random $n \times n$ symmetric matrix $\boldsymbol W$ drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form $\boldsymbol x^\top \boldsymbol…
We investigate the effective coupling between heat and fluid dynamics within a thin fluid layer in contact with a solid structure via a rough surface. Moreover, the opposing vertical surfaces of the thin layer are in relative motion. This…
For hexagonal nets, descriptive of {111} fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction,…
This thesis addresses the question of the maximal number of $d$-simplices for a simplicial complex which is embeddable into $\mathbb{R}^r$ for some $d \leq r \leq 2d$. A lower bound of $f_d(C_{r + 1}(n)) =…
The ability to engineer complex three-dimensional shapes from planar sheets with precise, programmable control underpins emerging technologies in soft robotics, reconfigurable devices, and functional materials. Here, we present a…
Curved thin sheets are ubiquitously found in nature and manmade structures. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state. This assumption, however, goes against…
Open-set 3D macromolecule detection in cryogenic electron tomography eliminates the need for target-specific model retraining. However, strict VRAM constraints prohibit processing an entire 3D tomogram, forcing current methods to rely on…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts…
We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…